This article examines a "calculus graphing schema" and the triad stages of schema development from Action-Process-Object-Schema (APOS) theory. Previously, the authors studied the underlying structures necessary for students to process concepts and enrich their knowledge, thus demonstrating various levels of understanding via the calculus…

This paper summarizes our analysis of the complexity of ratio problems at Grades 6 and 7, and reports a two-year experiment related to the teaching and learning of rational numbers and proportionality in these grades. Two classes were followed and observed. Part of the teaching material was common to both classes, mainly the objectives and the…

Prisoner's Dilemma is a common game theory scenario in which two players must choose between acting cooperatively or out of pure self-interest. What a player decides affects not only his own outcome but also that of the other player. "Friend or Foe," a TV game show that has appeared on the cable Game Show Network (GSN), places pairs of contestants…

As part of their course, the authors were asked to teach a mathematics lesson to a class of Y6 pupils. Since they did not know the pupils, they felt that the theme of the session was of the utmost importance, so they chose something which they hoped would stimulate the pupils' imagination and entice them into the session. They wanted to use…

In this study, we consider the potential of multimedia cases as tools for teacher professional development. Specifically, we examined online and face-to-face discussions that occurred within groups composed of pre-service mathematics teachers, in-service mathematics teachers, mathematicians, and mathematics teacher educators. Discussions within…

This book provides ideas, practical suggestions, and blackline masters to present mathematics concepts using cooperative learning activities in the primary grades. The first sections explain how to make cooperative learning part of the curriculum and include an overview, instructions, and activities for introducing cooperative learning to students…

This book explores a class of geometric patterns called tessellations, a pattern made up of one or more shapes which completely cover a surface without any gaps or overlaps. Focus in on one of the more elementary types of tessellations and investigation of them through concepts basic to art, geometry, and design. The seven chapters look at which…

The issue of how a child constructs higher order, logical mathematical intelligence within the context of a multiple-intelligences classroom is explored in this story. Teacher journal observations of one 5th-grade child are woven with selected literature on multiple intelligences and research trends in elementary mathematics education. The story…

The National Assessment of Educational Progress (NAEP) provides data about what children know and can do with the goal of using this information to improve education. This book contains interpretive reports based on results from the mathematics assessments conducted by the NAEP regarding: (1) the cognitive performance of students at grades 4, 8,…

This book is a compilation of recent research on the development of multiplicative concepts. The sections and chapters are: (1) Theoretical Approaches: "Children's Multiplying Schemes" (L. Steffe), "Multiplicative Conceptual Field: What and Why?" (G. Vergnaud), "Extending the Meaning of Multiplication and Division" (B. Greer); (2) The Role of the…

Designed as an avenue of communication for mathematics educators concerned with the views, ideas, and experiences of two-year college students and teachers, this journal contains articles on mathematics exposition and education, and regular features that present book and software reviews and math problems. The first of two issues of volume 9…

Students can learn to solve problems of qualitative integration and differentiation independently of their study of formal calculus or algebra. This exploratory study investigated the basic intuitions that elementary school children construct in their daily experience with physical and symbolic change. Elementary school children (n=18) were…

This study was designed to: (1) outline briefly the meaning and importance of the family of concepts stemming from the ideas of estimation, approximation, checking, and precision; (2) survey the present place of such concepts in the curriculum; and (3) relate the teaching and learning of these concepts to the availability of the calculator as an…

A model for multiplication is described and used to discuss the properties of division. (SD)

It is a well-known fact that the idea of function plays a unifying role in the development of mathematical concepts. Yet research has shown that many students do not understand it adequately even though they have experienced a great deal of success in performing a plethora of operations on function, and on using functions to solve various types of…